From: John Conover <john@email.johncon.com>
Subject: Re: forwarded message from John Conover
Date: Fri, 1 Nov 1996 15:25:52 -0800
John Conover writes:
>
> Yesterday, Garzarelli reiterated her prediction that the U.S. stock
> market will crash right after the elections. Today, the UBS reiterated
> their prediction that it won't:
>
> SINGAPORE - Contrary to popular belief, the U.S. stock
> market is not on the verge of a crash or even major correction,
> Union Bank of Switzerland (UBS) said.
> Based on price earnings (PE) ratios, the U.S. equity markets
> were only slightly overvalued at the moment, a group of UBS
> economists told a briefing in Singapore.
>
> John
>
So, we have two very respected institutions, Garzarelli and UBS, with
a very impressive set of credentials and historical track records,
making conflicting predictions. There is also substantial evidence
that there is a 58%, or so, chance that Garzarelli will be correct,
and a 42% chance that the UBS will be correct. Of what use is that?
Well it appears to present a bit of dilemma, since if you sell your
portfolio, there is a 48% chance that the market will moved up, and
you would not have participated in it, (ie., you would have lost
money.) Likewise if you keep your portfolio, there is a 52% chance
that you will loose money when the market moves down. Sounds like a
probabilistic loose-loose scenario, huh? Not really.
If you look at the probabilities, something like Garzarelli is
predicting will happen every 741 business days, (ie., 3 sigma,) on
average-a probabilistic number that has not changed since the
U.S. Civil war. (We don't have records prior to that-but the same
phenomena was observed in Holland in the 1600's when folks were
investing heavily in tulip bulbs.) So, if you are an investor, you
better have some prescription on how to address such issues.
Modern economics theory does not look for underlying causes of these
"surprises" in the equity markets. Here's why. Markets are considered
to be something akin to pyramid games. For example, it is not P/E
ratios that are important, per se, but the perceptions of the many
agents participating in the market concerning the effect that P/E
fluctuations has on their investment value, that determines the market
dynamics. So, really, the market dynamics are caused by the agent's
perceptions of the other agent's perceptions-which is
self-referential.
In modern economic theory, the perceptions of the agents are allowed
to differ, as in the case of Garzarelli and the UBS. If we permit many
agents to interact in the market, based on their perceptions of
other's perceptions, it can be shown that[1]:
1) Since it is self-referential, the market investment process
exhibits Godelian phenomena, ie., there is no "model" of the
market that can be proposed that is consistent and complete[3
pp. 2]. (As a passing note, this indeterminacy is by no means an
anomaly. On the contrary, it pervades all of economics and game
theory[3 pp. 3].)
2) The market graph will be the same as a random walk, ie., a
fractional Brownian fractal[1 pp. 29, 42][2 pp. 6][3 pp. 6]. This
is a result of the dynamics of many agents operating on the
market, each with different perceptions and expectations.
It is the last statement that is the most important in our efforts to
find a prescription on how to address "surprises" in the equity
markets. Note that the last statement says that whatever we do, it
will be done in a "noisy" environment, (fractional Brownian noise, to
be exact.) Note, also, that this noise is caused by, or causes, (it is
impossible to tell which-the first statement says that cause and
effect are not distinguishable,) some agents to make decisions that
other agents would consider inappropriate, based on their perceptions
and experience. These two notes are very important concepts-and mean
that the nature of the problem is information-theoretic. So, we now
have multiple agents, each gaining information from a noisy
environment, and making decisions on, (possibly incomplete,)
information about the environment, and acting on those decisions,
which in turn, affect the environment. Exactly the kind of thing that
information theory was designed to handle[4].
And what does information theory tell us we should do? If we know the
probability of making a correct decision in our noisy environment, we
can calculate what the optimum fraction of our portfolio that should
be invested in the equity markets. Obviously, we should not invest the
entire portfolio, since if Garzarelli is correct, we would loose
everything just after the election. Likewise, we should have some
fraction of our portfolio invested, since if the UBS is correct, we
could make money. Note that what we have to do is to SIMULTANEOUSLY
maximize our gains and minimize our losses, (ie., exposure.) And how
do we do that?
If you measure the probability, p, of an agent making a correct
decision, you will find it is 54% for the equities market. From
information theory, (symmetric binary channel in a Brownian noise
environment,) the optimum fraction of the portfolio to invest at any
time, f, is:
f = 2p - 1
or f = 8%. Note that it does not make any difference whether
Garzarelli or the UBS is correct. (I didn't say the Garzarelli/UBS
affair wasn't interesting, just that if you manage your portfolio
right, it doesn't make any difference who i wins.) And, what else does
information theory say about investing in multiple agent markets that
create noise-ie., pyramid games?
If we set up a simple model, where we have many alternatives of
investment, and all investment markets are multiple agent markets with
noise, and for simplicity, assume that p is the same for all markets,
and equal to 54%, (not an unreasonable first order approximation in
capitalist markets, by the way,) then:
1) Your investment portfolio should be made up of 12 categories,
ie., currency, stocks, bonds, metals, etc. (Fancy that, just what
CFO's know from experience.) So, how mutual funds compare with
that when their diversity is only 2-stocks and bonds. (Hint, look
at the pro forma of the top 50 mutual funds and compare them to
the DJIA and S&P for the last fifteen years. You would have done
much better by playing f = 2p - 1, and selecting your stocks with
a dart thrown across the room at the WSJ.)
2) The stock category should consist of 12 stocks. (Fancy that,
just what the brokers know from experience.) Naturally, you will
find folks that made a killing in the last two years. (Which is
not surprising, since it would have been difficult to loose
money-not impossible, but difficult.) Ask them how they did in
October of 1987. The folks doing f = 2p - 1 did very well, under
the circumstances, and did extremely well the last two years,
also.
Note that p can be measured, dynamically, and your whole investment
portfolio can be administered automatically using only the formula f =
2p - 1. At least in this simple case.
Fancy that, we just invented programmed trading-note that it takes
into account the aggregate perceptions and cognitions of the agents,
and does not depend, per se, on anticipating what the market will
do-in point of fact, that is impossible. Note, also, that the it does
not depend on the market establishing an equilibrium for stock
prices-for that, also, is impossible. Why impossible? It would not be
a noisy environment if either were possible-and if you look at the
graph of any stock's price, it just looks noisy.
Now you have a prescription for handling the noise. (Whether it was
created by Garzarelli/UBS, or any other source for that matter.) Of
course now, if you have more that 8% of your investment portfolio
invested in stocks, then maybe you should be worrying.
John
BTW, if you are running more than 8%, don't feel bad. You have a lot
of company. Most of the PT's have been caving to greed the last two
years-but when Garzarelli/UBS announced their "fantasies," everyone
moved back to 8%-ASAP.
[1] "Nonlinear Time Series, Complexity Theory, and Finance," William
A. Brock and Pedro J. F. de Lima, To appear in "Handbook of
Statistics Volume 14: Statistical Methods in Finance," edited by
G. Maddala and C. Rao. New York: North Holland, forthcoming. Also
available from http://www.santafe.edu/sfi/publications.", March, 1995.
[2] "Competing Technologies, Increasing Returns, and Lock-In by
Historical Events," W. Brian Arthur, Econ Jnl, 99, pp. 106-131,
1989. Also available from http://www.santa.fe.edu/arthur, June, 1988.
[3] "Complexity in Economic and Financial Markets," W. Brian Arthur,
Complexity, 1, pp. 20-25, 1995. Also available from
http://www.santa.fe.edu/arthur, February, 1995.
[4] "A New Interpretation of Information Rate," Bell System Tech. J.,
vol. 35, pp. 917-926, 1956.
--
John Conover, john@email.johncon.com, http://www.johncon.com/